The sum of the ages of the father and his son is 100 years now 5 years ago their ages were in the ratio of 2:1. The ratio of the ages of the father and son after 10 years will be ____?

4:3

5:3

10:7

None of these

Current sum of ages = 100 years

5 years ago, their ages were in the ratio of 2:1. Let's call the father's age 5 years ago "2x" and the son's age 5 years ago "x".

We know that 5 years ago, their sum of ages was:

2x + x = 3x

Since the current sum of ages is 100, we can set up an equation:

(2x + 5) + (x + 5) = 100

Combine like terms:

3x + 10 = 100

Subtract 10 from both sides:

3x = 90

Divide by 3:

x = 30

So 5 years ago, the father's age was 2x = 60 and the son's age was x = 30.

Now, let's find their ages after 10 years:

Father's age = 60 + 5 + 10 = 75

Son's age = 30 + 5 + 10 = 45

The ratio of their ages after 10 years is:

75:45 = 5:3